8 research outputs found
Parallel spinors and holonomy groups
In this paper we complete the classification of spin manifolds admitting
parallel spinors, in terms of the Riemannian holonomy groups. More precisely,
we show that on a given n-dimensional Riemannian manifold, spin structures with
parallel spinors are in one to one correspondence with lifts to Spin_n of the
Riemannian holonomy group, with fixed points on the spin representation space.
In particular, we obtain the first examples of compact manifolds with two
different spin structures carrying parallel spinors.Comment: 10 pages, LaTeX2
Homogeneous heterotic supergravity solutions with linear dilaton
I construct solutions to the heterotic supergravity BPS-equations on products
of Minkowski space with a non-symmetric coset. All of the bosonic fields are
homogeneous and non-vanishing, the dilaton being a linear function on the
non-compact part of spacetime.Comment: 36 pages; v2 conclusion updated and references adde
Randomizing world trade. II. A weighted network analysis
Based on the misleading expectation that weighted network properties always
offer a more complete description than purely topological ones, current
economic models of the International Trade Network (ITN) generally aim at
explaining local weighted properties, not local binary ones. Here we complement
our analysis of the binary projections of the ITN by considering its weighted
representations. We show that, unlike the binary case, all possible weighted
representations of the ITN (directed/undirected, aggregated/disaggregated)
cannot be traced back to local country-specific properties, which are therefore
of limited informativeness. Our two papers show that traditional macroeconomic
approaches systematically fail to capture the key properties of the ITN. In the
binary case, they do not focus on the degree sequence and hence cannot
characterize or replicate higher-order properties. In the weighted case, they
generally focus on the strength sequence, but the knowledge of the latter is
not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243
[physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011
New non compact Calabi-Yau metrics in D=6
A method for constructing explicit Calabi-Yau metrics in six dimensions in
terms of an initial hyperkahler structure is presented. The equations to solve
are non linear in general, but become linear when the objects describing the
metric depend on only one complex coordinate of the hyperkahler 4-dimensional
space and its complex conjugated. This situation in particular gives a dual
description of D6-branes wrapping a complex 1-cycle inside the hyperkahler
space, which was studied by Fayyazuddin. The present work generalize the
construction given by him. But the explicit solutions we present correspond to
the non linear problem. This is a non linear equation with respect to two
variables which, with the help of some specific anzatz, is reduced to a non
linear equation with a single variable solvable in terms of elliptic functions.
In these terms we construct an infinite family of non compact Calabi-Yau
metrics.Comment: A numerical error has been corrected together with the corresponding
analysis of the metri
A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds and
. We also discuss regular metrics on non-compact manifolds in eleven
dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra
3-Sasakian geometry, nilpotent orbits, and exceptional quotients
Using 3-Sasakian reduction techniques we obtain infinite families of new 3-Sasakian manifolds M (p(1), p(2), p(3)) and M (p(1), p(2), p(3), p(4)) in dimension 11 and 15 respectively. The metric cone on (p(1), p(2), p(3)) is a generalization of the Kronheimer hyperkahler metric on the regular maximal nilpotent orbit of sl (3, C) whereas the cone on M (p(1), p(2), p(3), p(4)) generalizes the hyperkahler metric on the 16-dimensional orbit of so(6, C). These are the first examples of 3-Sasakian metrics which are neither homogeneous nor toric. In addition we consider some further U(1)-reductions of M(p(1), p(2), p(3)). These yield examples of nontoric 3-Sasakian orbifold metrics in dimensions 7. As a result we obtain explicit families O(Theta} of compact self-dual positive scalar curvature Einstein metrics with orbifold singularities and with only one Killing vector field